The following questions are about the function f(x,y)=x^{2}e^{2xy}.

Kyran Hudson 2021-10-23 Answered
The following questions are about the function f(x,y)=x2e2xy.
Find an equation of the tangent plane of f at the point (2,0, f(2,0))=(2,0,4).
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Expert Answer

Tasneem Almond
Answered 2021-10-24 Author has 91 answers
Step 1
If f(x,y) is a function of two variables x and y, then
fx(x,y)=fx
fy(x,y)=fy
The equation of the tangent plane of function f at the point (x0,y0) is
z=f(x0,y0)+fx(x0,y0)(xx0)+fy(x0,y0)(yy0)
Step 2
The value of the given function at (2,0) is
f(2,0)=(2)2e2(2)(0)
=4e0
=4(1)
=4
The equation of the tangent plane of function f at the point (2,0) is
z=f(2,0)+fx(2,0)(x2)+fy(2,0)(y0)
z=4+4(x-2)+16(y)
z=4+4x-8+16y
z=4x+16y-4
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Jeffrey Jordon
Answered 2022-08-15 Author has 2313 answers

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